Crystals 2019, 9, 541; doi:10.3390/cryst9100541 www.mdpi.com/journal/crystals

Article

Crystal-Chemical Properties of Synthetic Almandine-Pyrope Solid Solution by X-Ray Single-Crystal Diffraction and Raman Spectroscopy Yunqian Kuang 1,2,3, Jingui Xu 4, Bo Li 1,2, Zhilin Ye 1,2, Shijie Huang 1,2, Wei Chen 1,2,5, Dongzhou Zhang 4, Wenge Zhou 1,* and Maining Ma 6,*

1 Key Laboratory for High-Temperature and High-Pressure Study of the Earth’s Interior, Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550081, China; kuangyunqian@126.com (Y.K.); fenberlee@163.com (B.L.); cugbyezhilin@163.com (Z.Y.); roberthuang1996@126.com (S.H.); chen123wei860701@163.com (W.C.)

2 University of Chinese Academy of Sciences, Beijing 100049, China 3 Bureau of Natural Resources and Planning of Yongzhou, Yongzhou 425000, China 4 Hawaii Institute of Geophysics and Planetology, School of Ocean and Earth Science and Technology,

University of Hawaii at Manoa, Honolulu, Hawaii 96822, USA; xujingui1990@126.com (J.X.); dzhang@hawaii.edu (D.Z.)

5 Guizhou Polytechnic of Construction, Guiyang 551400, China 6 Key Laboratory of Computational Geodynamics, College of Earth and Planetary Sciences, University of

Chinese Academy of Sciences, Beijing 100049, China * Correspondence: zhouwenge@vip.gyig.ac.cn (W.Z.); mamn@ucas.ac.cn (M.M.)

Received: 31 August 2019; Accepted: 17 October 2019; Published: 19 October 2019

Abstract: Crystal-chemical properties of synthetic Almandine-Pyrope (Alm-Pyr) solid solutions were investigated by X-ray single-crystal diffraction and Raman spectroscopy. Garnet solid solution with different compositions were synthesized from powder at 4.0 GPa and annealed at 1200 °C for 48 h by a multi-anvil pressure apparatus. Garnet crystals with different sizes (about 60-1000 μm) were obtained from synthesis. The results of X-ray single-crystal diffraction show that the unit cell constants decrease with increasing Pyr contents in the synthetic Alm-Pyr crystals due to the smaller ionic radius of Mg2+ in eightfold coordination than that of Fe2+. The data exhibit obviously positive deviations from ideal mixing volumes across the Alm-Pyr join which may be caused by the distortion of the SiO4 tetrahedron. Moreover, the significant decrease in the average M-O bond length and volume of the [MgO8]/[FeO8] dodecahedron with increasing Pyr contents are the most important factors to the decrease in the Alm-Pyr crystal unit cell constant and volume. On the other hand, selected bond distances (average <M-O>, <Al-O>, and <D-O> distances) have a linear correlation with the unit-cell parameter, but the <Si-O> distance has nonlinear correlation. With increasing the unit-cell parameter, the average <M-O> distance increases significantly, followed by the average <D-O> and <Al-O> distances. While the <Si-O> distance changes negligibly further confirming the conclusion that the significant decrease of the average M-O bond length of the [MgO8]/[FeO8] dodecahedron with increasing Pyr contents are the most important factors to the decrease in the Alm-Pyr crystal unit cell volume. In the Raman spectra collected for the Alm-Pyr solid solutions, Raman vibration mode assignments indicate that the Raman vibrational spectra change along the Alm-Pyr binary solution. The mode frequencies of Si-O stretching, Si-O bending, and the rotation of the SiO4-tetrahedron (R(SiO4)) decrease linearly, while the translational modes of the SiO4-tetrahedron (T(SiO4)) increase with increasing Alm contents.

Keywords: synthetic almandine-pyrope solid solution; crystal-chemical property; X-ray single-crystal diffraction; Raman spectroscopy

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1. Introduction

Garnet is not only one of the most important mineral in the upper mantle [1], but also an important phase in metamorphic rocks [2]. Hence, garnet is stable over a wide range of pressures and temperatures in the Earth. In addition, garnet plays a prominent role in many geothermobarometers used to calculate the pressure and temperature of the mantle and metamorphic rock [3,4]. Therefore, the crystal-chemical properties concerning the elastic-strain, thermodynamic and trace-element substitution behavior of garnet are important for constraining the compositions, thermodynamic and physical properties of rocks in the middle-low crust and upper mantle.

The garnet group is a variety of nesosilicate minerals with an isolated group of [SiO4] as its basic skeleton, including all garnets of essentially the same structure and chemically similar elements, and belongs to the cubic system and space group 𝐼𝑎3𝑑. The general formula for the garnet group is X3Y2Z3O12, where X, Y, and Z refer to dodecahedral, octahedral, and tetrahedral sites, respectively [5] (Figure 1). Generally, the X site is occupied by Mg2+, Fe2+, Mn2+, Ca2+, etc. The Y site is occupied by Al3+, Fe3+, Cr3+, Ti4+, etc. Si4+ and Al3+ occupy the Z site. The minerals of the garnet group are divided into two series, pyralspite and ugrandite, depending on the cation in the X site. If the X site of garnet is mainly occupied by Mg2+, Fe2+, and Mn2+, it is pyralspite, while if the X site is mainly occupied by Ca2+, it is ugrandite. However, most of garnet group samples in nature occur as multi-component solid solutions. For example, the pyrope (Pyr) component of garnet found in diamonds of peridotitic and eclogitic origin can be as high as about 79 mol.% and 43 mol.%, respectively, and the almandine (Alm) component is about 11 mol.% and 33 mol.%, respectively [6].

Figure 1. Crystal structure of garnet at ambient conditions.

The structure, elastic properties, and electrical conductivity of garnet end-members have been extensively studied, but detailed studies on structure by X-ray single-crystal diffraction and Raman spectroscopy of garnet solid solutions are limited. In particular, Raman spectroscopy studies have only focused on grossular-andradite join, pyrope-grossular join, and almandine-pyrope (Alm-Pyr) join [7-10]. To date, even in the most studied Alm-Pyr join, the structural properties of Alm-Pyr solid solution by the X-ray single-crystal diffraction are very limited, only several garnet compositions along the Alm-Pyr solid solution have been investigated by the X-ray single-crystal diffraction in details [11]. However, only when the strictly binary solid-solution compositions are available can we fully understand how the natural garnet structure changes as a function of composition. Therefore, the crystal-chemical properties of the Alm-Pyr solid solution require further systematic research.

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In this study, we firstly synthesize 11 garnet compositions along the Alm-Pyr solid solution at high pressure and high temperature. Then we select 10 garnets for X-ray single-crystal diffraction and 9 garnets for Raman spectroscopy studies. Finally, we discuss the effect of composition on the crystal-chemical properties along the Alm-Pyr binary.

2. Experiments

2.1. Crystal Synthesis

Eleven single crystals of Alm-Pyr garnet (Alm100, Pyr9Alm91, Pyr14Alm86, Pyr23Alm76, Pyr31Alm68, Pyr48Alm52, Pyr57Alm43, Pyr67Alm32, Pyr78Alm22, Pyr87Alm12, and Pyr100) used in this study were synthesized at high pressure and high temperature using a multi-anvil pressure apparatus (YJ-3000t) at the Institute of Geochemistry, Chinese Academy of Sciences, Guiyang, China. The sample assembles and synthesis process were similar to those used by Fan et al. (2017) and Xu et al. (2018) [12,13], and were briefly described here.

The starting materials used in the synthesizing experiments were stoichiometric amounts of high-purity magnesium oxide (MgO), aluminum oxide (Al2O3), silica (SiO2), Iron (Fe), and Ferric oxide (Fe2O3). The mixture was grounded in acetone at an agate mortar for 3 h and then heated for more than 12 h at 200 °C in a muffle furnace to eliminate adsorbed water. Finally, the mixture was encapsulated in the platinum capsules with 1 weight percent (wt.%) of deionized water. The graphite tube was used as the heater and the pressure transmitting medium was pyrophyllite. All complete assemblies were heated for more than 10 h at 200 °C in a muffle furnace before being loaded into the apparatus.

The sample assembly was first compressed to 4.0 GPa for over 20 min by a multi-anvil pressure apparatus (YJ-3000t) and then heated to 1200 °C in 20 min. After a run duration of 48 h, the garnet crystals with different sizes (about 60–1000 μm) were obtained from the quenched run product.

2.2. Analysis Methods

The synthetic single garnet crystals were observed by the stereoscopic microscope. The compositions of garnet crystals with sizes larger than ~100 μm were performed at the

Institute of Geochemistry, Chinese Academy of Sciences, Guiyang, China with an electron microprobe analysis (EMPA, JEOL Hyperprobe JXA-8500F microscope), operating at a 15 kV accelerating voltage, 20 nA beam current, and a beam size of 10 μm.

The synchrotron X-ray single-crystal diffraction experiments at ambient condition were carried out with a six-circle diffractometer at 13-BM-C experimental station of the Advanced Photon Source, Argonne National Laboratory. The wavelength of the incident X-ray was 0.4340 Å, and the beam size was 12 μm × 18 μm. Diffraction images were acquired on Dectris Pilatus 1M detector and calibrated using the ambient LaB6 as the diffraction standard [14]. Stepped φ rotation exposures were collected for the single-crystal sample of different components, with an exposure time of 1 s/deg. The φ-rotation (from −170° to 170°) axis was horizontal and perpendicular to the incident X-ray direction. The diffraction images were analyzed using the Bruker APEX3 software. Crystal structures were refined from the intensity data using the SHELXL software, facilitated by Olex 2 user interfaces [15,16]. Table S1 in the supplements shows the unit-cell parameters and details of the structural refinement of the samples.

Raman spectra in this study were collected with the Renishaw Raman spectrometer equipped with a Peltier-cooled charge-coupled device (CCD) detector. The laser exciting the sample was 532 nm in wavelength. The laser light was focused on samples by using the Leica microscope with a long-distance 20× objective to a beam size of about 2 μm diameter and the laser power was 2 mW. Each Raman spectrum was collected with a total exposure time of 300 s. Nine spectra were collected from different points on each garnet sample and measured Raman data from 100 cm−1 to 1200 cm−1. We fitted the Raman peaks and obtained peak parameters, Raman mode frequencies, and peak widths [full width at half-maximum (FWHM)] from these spectra.

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3. Results and Discussion

3.1. Synthetic Garnet Crystal

The microphotographs of the synthetic Alm-Pyr crystals are shown in Figure 2 and Figure S1 in the supplements. The synthetic Alm-Pyr crystals are available in a variety of colors and optical characteristics. The color of the crystals gradually changes from colorless to orange and maroon with the increase of Alm contents in the Alm-Pyr crystals from 0 mol.% to 100 mol.%. In the meantime, the Alm-Pyr crystals also gradually vary from transparent to translucent, and finally to nearly opaque. The typical dimension of Alm-Pyr crystals with granular forms ranges from about 60 μm up to more than 1 mm with the increase of Alm contents (Figure 2).

Figure 2. Typical microphotographs and dimensions of Alm-Pyr crystals synthesized in this study with increasing Alm contents.

The Alm-Pyr crystals have different grain size and morphology because the anisotropy of the growth fronts depends on the chemical composition [17] (Figures 2 and S1). The microphotographs show that the largest grains are from sample Alm100 having a size of about 1000 μm. All samples have a combined form of rhombic dodecahedron {110} and tetragonal trisoctahedron {211}. Moreover, the faces of rhombic dodecahedron are more developed than those of tetragonal trisoctahedron (Figure S1).

3.2. Chemical Composition

All the 11 synthetic garnet compositions along the Alm-Pyr solid solution are given in Table 1. In addition, garnet crystal-chemical formulae were calculated according to the recommendations of Grew et al. (2013) [18] and also reported in Table 1.

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Table 1. Garnet compositions along the pyrope–almandine solid solution.

Nominal Compositions

Alm100 Pyr10Alm90 Pyr20Alm80 Pyr30Alm70 Pyr40Alm60 Pyr50Alm50 Pyr60Alm40 Pyr70Alm30 Pyr80Alm20 Pyr90Alm10 Pyr100

EMPA Compositions

Alm100 Pyr9Alm91 Pyr14Alm86 Pyr23Alm76 Pyr31Alm68 Pyr48Alm52 Pyr57Alm43 Pyr67Alm32 Pyr78Alm22 Pyr87Alm12 Pyr100

wt.% of oxides SiO2 35.76 (27) 36.83 (102) 36.37 (175) 36.26 (177) 38.33 (26) 38.88 (174) 40.11 (57) 41.21 (28) 42.68 (59) 43.28 (33) 43.34 (101) TiO2 1.58 (147) 0.90 (75) 1.20 (112) 0.87 (67) 1.34 (4) 0.05 (5) 0.18 (22) 0.55 (55) 0.01 (1) 0.20 (4) 0.11 (12) Al2O3 19.81 (53) 20.10 (44) 20.25 (123) 19.96 (31) 21.15 (28) 21.57 (275) 22.23 (16) 22.72 (16) 22.20 (167) 24.13 (24) 24.36 (52) FeO 46.04 (72) 43.09 (15) 40.32 (95) 38.33 (234) 33.94 (38) 23.37 (147) 22.17 (70) 17.13 (22) 11.98 (37) 6.83 (200) 0.05 (5) MnO 0.01 (2) 0.01 (1) 0.01 (3) 0.01 (1) 0.02 (2) 0.01 (2) 0.02 (1) 0.01 (1) 0.01 (2) 0.00 0.01 (1) MgO 0.01 (1) 2.30 (21) 3.56 (94) 6.59 (158) 8.74 (22) 12.11 (74) 16.65 (69) 19.95 (48) 23.68 (72) 26.91 (162) 30.66 (37) CaO 0.02 (2) 0.03 (1) 0.05 (3) 0.07 (4) 0.10 (3) 0.07 (10) 0.09 (6) 0.14 (2) 0.15 (11) 0.11 (9) 0.01 (1) Total 103.23 (20) 103.26 (124) 101.76 (440) 102.08 (12) 103.62 (57) 96.10 (328) 101.44 (80) 101.72 (63) 100.72 (77) 101.46 (64) 98.54 (191)

mol.% of garnets Pyrope 0.05 (4) 8.68 (69) 13.56 (334) 23.41 (545) 31.37 (76) 47.83 (260) 57.09 (187) 67.25 (42) 77.59 (108) 87.30 (406) 99.88 (11)

Spessartine 0.03 (2) 0.03 (3) 0.03 (6) 0.01 (1) 0.04 (4) 0.03 (5) 0.03 (3) 0.02 (1) 0.03 (3) 0.00 0.01 (3) Grossular 0.04 (4) 0.08 (3) 0.13 (8) 0.18 (11) 0.26 (6) 0.20 (28) 0.23 (14) 0.34 (4) 0.36 (27) 0.26 (21) 0.02 (3)

Almandine 99.88 (8) 91.20 (69) 86.28 (333) 76.40 (532) 68.33 (83) 51.86 (286) 42.65 (172) 32.39 (45) 22.02 (104) 12.45 (384) 0.08 (9) Total 100.00 100.00 100.00 100.00 100.00 100.00.00 100.00.00 100.00 100.00 100.00 100.00

Chemical formula

Fe3.13Al1.90Ti0.

1Si2.91O12

(Fe2.88Mg0.27) Al1.89Ti0.05Si2.94

O12

(Fe2.71Mg0.43) Al1.92Ti0.07Si2.

92O12

(Fe2.55Mg0.78) Al1.87Ca0.01

Ti0.05Si2.88O12

(Fe2.16Mg0.9

9) Al1.9Ca0.01Ti0.08Si2.92O12

(Fe1.52Mg1.41) Al1.99Ca0.01Si3

.04O12

(Fe1.36Mg1.82) Al1.93Ca0.01

Ti0.01Si2.95O12

(Fe1.03Mg2.13) Al1.92Ca0.01Ti0

.03Si2.95O12

(Fe0.71Mg2.4

9) Al1.85Ca0.01

Si3.01O12

(Fe0.39Mg2.74)Al1.95Ca0.01Ti0

.01Si2.96O12

Mg3.12Al1.96 Ti0.01Si2.96O12

Atom occupancy

composition Alm100 Pyr11Alm90 Pyr16Alm84 Pyr28Alm73 Pyr41Alm60 Pyr45Alm55 Pyr52Alm48 Pyr67Alm33 Pyr75Alm24 Pyr100

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The EMPA results indicate that the synthesized garnet crystals consist almost entirely of Pyr and Alm, where the components of the Pyr and Alm are always greater than 99.6 mol.% and little grossular and spessartine (<0.4 mol.%) are also presented (Table 1). However, as shown in the Figure 3, except for the end members of Alm and Pyr garnets, the compositions of the other 9 synthetic Alm-Pyr crystals are obviously different from the nominal compositions of the starting material with Pyr contents less than those of nominal compositions (Figure 3). The result is basically consistent with occupancy factors obtained by structural refinement of the samples (Tables 1 and S1). Expect for the samples with 10 mol.% and 40 mol.% Pyr in nominal composition and the end members of Alm and Pyr garnets, the measured compositions of the other 6 synthetic Alm-Pyr crystals are obviously different from the nominal compositions of the starting material with Pyr contents less than those of nominal compositions (Figure 3).

Figure 3. Relation between the measured composition and nominal composition for Alm-Pyr crystals.

3.3. Characteristics of Unit-Cell Parameters

The unit-cell parameters and the unit-cell volumes of the Alm-Pyr Crystals refined from the X-ray single-crystal diffraction are summarized in Table 2, along with the results of the previous studies for comparison [11,19,20,23]. Our results clearly showed that the unit cell constants decrease systematically with increasing Pyr contents in the synthetic Alm-Pyr crystals, due to the smaller ionic radius of Mg2+ in eightfold coordination (0.89 Å) than that of Fe2+ (0.92 Å) (Figure 4) [21].

The unit-cell measurements on the Alm-Pyr solid solutions exhibited considerably more scatter and positive deviations from ideal volumes of mixing across the Alm-Pyr join (Figure 4), which is contrary to the results obtained by the X-ray powder diffraction previously [22,23]. In theory, any solid solution deviates from the ideal solution properties to some extent. In the present case, the

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rotation of the SiO4 tetrahedra is a possible cause of the positive deviations from ideal mixing volumes.

Figure 4. Unit cell constants versus the pyrope mol.% in Alm-Pyr crystals; The data of the previous studies are from the references of Takahashi et al. (1970) [20], Huang et al. (2014) [19], Milani et al. (2015) [11] and Geiger et al. (1997) [23].

Table 2. Unit-cell parameters and unit-volumes for almandine-pyrope crystals in this and previous studies a.

Composition Pry% a (Å) V (Å3) Reference Alm100 0 11.5320 (5) 1533.52 Takahashi et al. 1970 [20] Alm100 0 11.5330 (5) 1533.61 Takahashi et al. 1970 [20] Alm100 0 11.5303 (1) 1532.91 (4) This study Alm100 0 11.530 1533.52 (10) Milani et al. 2015 [11] Alm100 0 11.5291 (3) 1532.45 Geiger et al. 1997 [23]

Pyr7Alm93 7 11.5227 (2) 1529.90 Geiger et al. 1997 [23] Pyr9Alm91 9 11.5270 (1) 1531.62 (4) This study Pyr14Alm86 14 11.5241 (3) 1530.46 (12) This study Pyr15Alm85 15 11.51570 (2) 1527.63 Geiger et al. 1997 [23] Pyr22Alm72 22 11.5230 (5) 1530.02 Takahashi et al. 1970 [20] Pyr23Alm76 23 11.5276 (2) 1531.85 (6) This study Pyr25Alm75 25 11.5105 (2) 1525.045 Geiger et al. 1997 [23] Pyr30Alm70 30 11.5121 (3) 1526 (1) Huang et al. 2014 [19] Pyr31Alm68 31 11.5105 (1) 1525.06 (2) This study Pyr40Alm60 40 11.4995 (2) 1520.677 Geiger et al. 1997 [23] Pyr48Alm52 48 11.5096 (1) 1524.67 (2) This study Pyr50Alm50 50 11.4925 (3) 1517.90 Geiger et al. 1997 [23] Pyr54Alm46 54 11.4859 (1) 1515 (2) Huang et al. 2014 [19] Pyr57Alm43 57 11.5013 (4) 1521.39 (16) This study Pyr60Alm40 60 11.488 1516.32 (13) Milani et al. 2015 [11] Pyr60Alm31 60 11.521 (1) 1529.22 Takahashi et al. 1970 [20] Pyr62Alm38 62 11.4830 (2) 1514.14 Geiger et al. 1997 [23]

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Pyr67Alm32 67 11.4887 (3) 1516.40 (12) This study Pyr75Alm25 75 11.4737 (2) 1510.46 Geiger et al. 1997 [23] Pyr78Alm22 78 11.4802 (1) 1513.04 (3) This study Pyr83Alm17 83 11.4650 (3) 1511 (1) Huang et al. 2014 [19] Pyr90Alm10 90 11.4612 (2) 1505.53 Geiger et al. 1997 [23]

Pyr100 100 11.4552 (1) 1503.18 (4) This study Pyr100 100 11.4555 (3) 1503.29 Geiger et al. 1997 [23] Pyr100 100 11.4540 (5) 1502.70 Takahashi et al. 1970 [20] Pyr100 100 11.463 1506.15 (16) Milani et al. 2015 [11]

a. The data from Milani et al. (2015) [11] and this study were obtained by the single-crystal X-ray diffraction, while the other data from Takahashi et al. (1970) [20], Geiger et al. (1997) [23], and Huang et al. (2015) [19] were obtained by the powder X-ray diffraction.

Table 3 shows the bond lengths of average M-O (M is the cation in X site), Al-O, Si-O, D-O (D-O is the average distance from the four-coordinated O atom), and volumes of the [MgO8]/[FeO8] dodecahedron, the [AlO6] octahedron, the [SiO4] tetrahedron with different compositions along the Alm-Pyr join. We found that the average Si-O bond length of the [SiO4] tetrahedron changes negligibly with increasing pyrope mol.%, while the variation of the volume is less than 0.014 Å3. The variations of the average Al-O bond length and volume of [AlO6] octahedron with increasing pyrope mol.% are similar to those of the [SiO4] tetrahedron (Table 3). However, the behaviors of the average M-O bond length and volume with the increase in the pyrope molar fraction for the [MgO8]/[FeO8] dodecahedron are quite different from those of the [SiO4] tetrahedron and [AlO6] octahedron. The average M-O bond length of the [MgO8]/[FeO8] dodecahedron decreases significantly (Figure 5). Moreover, the decrease in the volume of the [MgO8]/[FeO8] dodecahedron with the Pyr content is important for interpreting the decrease in the unit cell volume with the Pyr content, while the other factors, such as the distortion of the polyhedrons and the decrease in the [SiO4] tetrahedron and the [AlO6] octahedron volumes, may be secondary in importance.

Figure 5. Average M-O bond length of [MgO8]/[FeO8] dodecahedron versus the pyrope mol.%. M represents the Mg2+ or Fe2+.

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Table 3. Selected bond distances (Å) for almandine-pyrope garnet samples in this study.

Bond Distances Alm100 Pyr9Alm91 Pyr14Alm86 Pyr23Alm76 Pyr31Alm69 Pyr48Alm52 Pyr57Alm43 Pyr67Alm32 Pyr78Alm22 Pyr100 M-O bond I length 2.2241 (9) 2.2218 (10) 2.2193 (12) 2.2203 (9) 2.2159 (9) 2.2153 (6) 2.2140 (9) 2.2088 (8) 2.2057 (7) 2.1993 (8) M-O bond I length 2.3701 (10) 2.3704 (10) 2.3680 (12) 2.3662 (9) 2.3606 (9) 2.3598 (7) 2.3599 (9) 2.3532 (8) 2.3501 (7) 2.3400 (7)

Average <M-O> 2.2971 (10) 2.2962 (10) 2.2936 (12) 2.2933 (9) 2.2882 (9) 2.2876 (7) 2.2853 (9) 2.2810 (8) 2.2779 (7) 2.2779 (7) [FeO8]/[MgO8] volume 20.836 20.82 20.754 20.736 20.599 20.582 20.514 20.408 20.327 20.101

<Al-O> 1.8918 (10) 1.8907 (11) 1.8931 (13) 1.8954 (10) 1.8925 (10) 1.8913 (7) 1.8912 (10) 1.8901 (8) 1.8903 (7) 1.8860 (8) [AlO6] volume 9.021 9.004 9.038 9.07 9.027 9.01 9.007 8.99 8.991 8.926

<Si-O> 1.6360 (10) 1.6360 (10) 1.6353 (13) 1.6360 (10) 1.6357 (10) 1.6370 (7) 1.6359 (10) 1.6349 (8) 1.6340 (7) 1.6350 (8) [SiO4] volume 2.206 2.205 2.201 2.204 2.202 2.207 2.202 2.197 2.192 2.195

a <D-O> 2.029 2.02977 2.0289 2.0295 2.02615 2.02588 2.02442 2.02175 2.02003 2.0151 a (Å) 11.53025 (9) 11.52701 (11) 11.5241 (3) 11.52759 (16) 11.51055 (6) 11.50955 (6) 11.5013 (4) 11.4887 (3) 11.48023 (8) 11.45522 (10)

a <D-O> = {(Si-O) + (Al-O) + (M1-O) + (M2-O)}/4, which is the average distance from the four-coordinated O atom.

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To eliminate the compositional variable, we also plot the bond distances versus the unit-cell parameter figures to the structural variations cross the Alm-Pyr solid solution. These figures show that the selected bond distances (average <M-O>, <Al-O>, and <D-O> distances) have a linear correlation with the unit-cell parameter, but the <Si-O> distance has nonlinear correlation which R2 = 0.284. With increasing the unit-cell parameter, the average <M-O> distance increases significantly, followed by the average <D-O> and <Al-O> distances. However, the <Si-O> distance change negligibly (Table 3, Figure 6). Comparing our data with the previous study of Antao et al. (2014), we can find that our synthetic samples match those of natural samples quite well (Figure 6) [24]. The average <D-O> distance present optimal linear with the unit-cell parameter of all the data and other bond distances show more scatter than that for the average <D-O> distance, which may mean that satisfactory coordination of the O atom is most important for the garnet structure.

Figure 6. Structural variations across the Alm-Pyr solid solution series. Black square represents data and solid trend lines (black) are the linear fit to data from this study and their equations are given as inserts. Red circle represents data and dashed trend lines (red) are the linear fit to data from the reference of Antao et al. (2014) [24].

3.4. Excess Mixing Volume in Solid Solutions

As we can see, the unit-cell measurements on the Alm-Pyr solid solutions in our study exhibited considerably more scatter and positive deviations from ideal volumes of mixing across the Alm-Pyr join, which shows non-ideal mixing properties (Figure 7). However, our results should show near-ideal mixing properties because of the small difference in ionic radii of Mg2+ (0.89 Å) and Fe2+ (0.92 Å) in eightfold coordination [21]. There are lots of possible factors that could have caused excess volume such as dampness, synthesizing some unidentified phase and the distortion of the SiO4 tetrahedra, etc. [9,25]. In this study, we think the cause might be the rotational orientation of the SiO4 tetrahedra. As mentioned above, satisfactory coordination of the O atom is most important for the garnet structure and the relationship between the average <M-O> distance and the unit-cell parameter has

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more excellent linearity than the bond distances of <Al-O> and <Si-O>. Figure 8 shows the polyhedron structural variations across the Alm-Pyr solid solutions. The bond distances of <M-O> and <Al-O> vary linearly with their polyhedron volumes, but the <Si-O> distance exhibits more scatter and deviation from linearity (Table 3). Moreover, SiO4 tetrahedra with the near-equal <Si-O> distance have different tetrahedra volumes, indicating the distortion of the SiO4 tetrahedron. The possible reason for this is the substitution of Mg2+ and Fe2+ cations in the dodecahedral sites. The smaller ionic radius of Mg2+ in eightfold coordination (0.89 Å) than that of Fe2+ (0.92 Å) causes the shorter Mg-O bond length than Fe-O bond length, then causes the distortion of the SiO4 tetrahedron. Therefore, we consider that the distortion of the SiO4 tetrahedron is a possible reason leading to excess volume in this study.

Figure 7. The excess volume versus the pyrope mol.%. Dashed lines (gray) is the polynomial fit to data.

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Figure 8. The polyhedron structural variations across the Alm-Pyr solid solutions. (a). The volume versus average M-O bond length of [MgO8]/[FeO8] dodecahedron, M represents the Mg2+ or Fe2+; (b).

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The volume versus Al-O bond length of [AlO6] octahedron; (c). The volume versus Si-O bond length of [SiO4] tetrahedron. Linear solid trend lines are fitted to data.

3.5. Characteristics of Raman Spectroscopy

Figure 9 shows the 9 Raman spectra collected from our Alm-Pyr solid solution series. Raman frequencies of peaks in these spectra and assigned Raman vibration modes are contained in Table 4. The peak positions in our study agree well with those of standard Raman spectra, and can be grouped into three distinct regions: low-frequency region between 167 cm−1 and 375 cm−1; medium energy peaks (475–688 cm−1); and high energy peaks (759–1060 cm−1). The symmetry for the total vibrational modes of garnet calculated by factor group analysis (FGA) is given as follows [26-28]:

Γtotal = 3A1g + 5A2g + 8Eg + 14F1g + 14F2g + 5A1μ + 5A2μ + 10Eμ + 18F1μ + 16 F2μ

A total of 25 Raman active (3A1g + 8Eg + 14F2g) and 17 infrared-active (17F1u) are expected. However, the observed vibrational modes are only 14 modes, which is less than the expected mode, and the peak around 330 cm−1~350 cm−1is mixed by J mode. The observed vibrational modes are grouped into three main regions (Figure 9). The highest frequency modes (A, B, C) are dominated by stretching motions of Si–O ((Si–O)str); the medium frequency modes at around 550 cm−1 (D, E, F, G, H) are dominated by bending motions of Si–O ((Si–O)bend); and the low-frequency modes are located at around 340 cm−1, 210 cm−1, and 168 cm−1. The modes at around 340 cm−1 (I, J, K) are dominated by rotation motions of SiO4 (R(SiO4)). In addition, the mode at around 210 cm−1 (L) is due to translational motions of SiO4 (T(SiO4)) [29]. The mode at around 168 cm−1(M) is due to the translation motion of Fe2+ [30], which appears in the samples with the Alm content higher than 52 mol.% (Figure 9).

Figure 9. Raman spectra of garnets along Alm-Pyr binary. The marked M peaks represent the newly appearing Raman modes (translational modes of X-cations) for Alm-rich garnets.

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Table 4. Raman mode frequencies (cm−1) of garnet solid solution along almandine-pyrope binary recorded at ambient condition.

Alm12Pyr87 Alm22Pyr78 Alm32Pyr67 Alm43Pyr57 Alm52Pyr48 Alm68Pyr31 Alm76Pyr23 Alm86Pyr14 Alm91Pyr9 Assignment Symmetry Species

Site Motion

1060 1057 1056 1045 1044 1041 1044 1035 1037 (Si-O)str F2g

v1 and v3 924 924 923 920 920 919 918 916 916 (Si-O)str A1g 867 867 867 866 865 865 864 (Si-O)str F2g

759 b F2g 688 a (Si-O)bend F2g

v2 and v4

644 644 642 638 637 635 634 633 630 (Si-O)bend F2g 587 586 584 581 (Si-O)bend Eg

560 560 559 558 557 556 555 555 556 (Si-O)bend A1g 507 508 506 503 503 501 500 499 500 (Si-O)bend F2g

486 482 481 481 478 478 475 (Si-O)bend F2g 375 375 374 370 372 372 367 370 365 R(SiO4) F2g

Rotation of SiO4 358 358 356 350 351 349 347 344 342 R(SiO4) A1g 350 351 353 333 332 323 329 R(SiO4) F2g 318 318 318 317 315 314 314 316 R(SiO4) F2g 209 209 210 210 209 211 211 214 213 T(SiO4) Eg Translation of SiO4

167 168 168 T(X2+) F2g Translation of X

cation a. Modes observed by Du (2018) [9], b. Modes observed by Peng (1994) [31] and Theodore (2013) [32].

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Figure 10 shows plots of different mode frequencies along Alm-Pyr binary. We can see that the Si-O stretching and Si-O bending modes frequencies decrease linearly with the Alm content. The A1g

spectra of the silicate garnets contain three modes around 350 cm−1, 550 cm−1 and 900 cm−1, and these modes have the maximum intensities. These selected A1g mode and Eg mode frequencies of SiO4

translation (T(SiO4)) as functions of composition along Alm-Pyr binary are shown in detail in Figure 11. The (Si-O)str modes show stronger dependence on composition than the (Si-O)bend. The Raman mode frequencies of the rotation of the SiO4-tetrahedron (R(SiO4)) decrease linearly with increasing Alm content, but the translational modes of the SiO4-tetrahedron (T(SiO4)) increase with increasing Alm content. The variation of the trends is attributed to a coupling between the vibrations of the translational modes of the SiO4-tetrahedron and those of the translational modes of the X-site cations [9,29].

Figure 10. Composition dependence of frequencies of Raman modes corresponding to internal motions of SiO4-tetrahedra: (a) Si–O stretching and (b) Si–O bending.

Figure 11. Selected Raman mode frequencies change with composition along Alm-Pyr binary. The solid lines are the linear fit results.

4. Conclusions

In summary, the crystal-chemical properties of the synthetic Alm-Pyr solid solution were carried out by X-ray single-crystal diffraction and Raman spectroscopy. Our results clearly show that the unit cell constants decrease with increasing Pyr contents (XPyr) in the synthetic Alm-Pyr crystals owing to

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the smaller ionic radius of Mg2+ in eightfold coordination (0.89 Å) than that of Fe2+ (0.92 Å). However, the data show considerably more scatter and positive deviations from ideal volumes of mixing across the Alm-Pyr join that may be caused by the distortion of the SiO4 tetrahedron. Furthermore, the results of the refined crystal structures show that the average M-O bond length and the volume of the [MgO8]/[FeO8] dodecahedron decrease significantly. Moreover, the results also indicate that the variations of the average M-O bond length and the volume of the [MgO8]/[FeO8] dodecahedron with the Pyr content are the key factors concerning the variations of unit cell constant and volume of the Alm-Pyr solid solution. On the other hand, the average <M-O>, <Al-O>, and <D-O> bond distances have a linear correlation with the unit-cell parameter, while the <Si-O> distance has nonlinear correlation. Furthermore, the average <D-O> distance present optimal linear with the unit-cell parameter of all the data and other bond distances show more scatter than that for the average <D-O> distance, which may mean that satisfactory coordination of the O atom is most important for the garnet structure.

In addition, Raman mode frequencies of garnets along the Alm-Pyr solid solution series show the vibrational spectra change with the composition. The Si-O stretching, Si-O bending, and the rotation of the SiO4-tetrahedron (R(SiO4)) mode frequencies decrease linearly, but the translational mode frequencies of the SiO4-tetrahedron (T(SiO4)) increase with the Alm content. The variation of the trends is a result of the coupling between the vibration of the translational mode of the SiO4-tetrahedron (R(SiO4)) mode and that of the translational mode of the X-site cations.

Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, Figure S1: Microphotographs of the synthetic Alm-Pyr crystals, Table S1: Details of the structural refinement of synthesis single garnet crystals. CSD 1950879-1950888 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge via http://www.ccdc.cam.ac.uk/conts/retrieving.html

Author Contributions: Conceptualization, W.Z. and M.M.; Methodology, W.Z.; Funding acquisition, J.X. and M.M.; Investigation, Y.K., J.X., B.L., S.H., D.Z. and W.Z.; data analysis, Y.K.; Writing—original draft, Y.K.; Writing—review & editing, Y.K., J.X., Z.Y., W.C. and W.Z. All authors discussed the results.

Funding: This project was supported by the National Natural Science Foundation of China (Grant No. 41772043, 41802043 and 41674089), the Joint Research Fund in Huge Scientific Equipment (U1632112) under cooperative agreement between NSFC and CAS, the Chinese Academy of Sciences “Light of West China” Program (Dawei Fan, 2017; Jingui Xu, 2019), Youth Innovation Promotion Association CAS (Dawei Fan, 2018434), and Innovation and Entrepreneurship Funding of High-Level Overseas Talents of Guizhou Province (Dawei Fan, [2019] 10).

Acknowledgments: The synchrotron single-crystal X-ray diffraction experimental work was conducted at GeoSoilEnviroCARS (Sector 13), Partnership for Extreme Crystallography program (PX^2), Advanced Photon Source (APS), and Argonne National Laboratory. The authors thank Yuanyun Wen for her assistance during Raman spectroscopy experiments.

Conflicts of Interest: The authors declare no conflict of interest.

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